Monopulse signal processor and method using same

ABSTRACT

A monopulse signal processor provides target monopulse ratios and thus target angles having an improved accuracy in those situations where a low signal-to-noise ratio subsists and the monopulse ratio is derived from a sequence of pulses. The monopulse ratio value is determined by: ##EQU1## and Σ Ii  is the in-phase component of the sum signal for the i th  pulse, Σ Qi  is the quadrature component of the sum signal for the i th  pulse, Δ Ii  is the in-phase component of the difference signal for the i th  pulse, and Δ.sub.Ωi is the quadrature component of the difference signal for the i th  pulse.

The Government has rights in this invention pursuant to Contract No. N00024-81-C-5145, awarded by the Department of the Navy.

The present invention relates to monopulse signal processors and more particularly to monopulse signal processors designed for operation with received signals having low signal-to-noise ratios.

A monopulse signal processing system determines the angle between the receive beam axis of a radio frequency (RF) antenna and a line to the apparent source of a received radio frequency signal. The received RF signal may have come directly from an active transmitter of that signal as in communications and direction finding applications or it may have been passively reflected by the apparent source as in radar applications. In radar applications, the radar system normally transmits the signal which reflects off the passive apparent source or "target". Hereinafter, both active sources and passive, reflecting "apparent" sources are included within the term "source", since the purpose of a monopulse system is to determine the point of origin of the waves impinging on its antenna. Because of the influence of the radar origin of monopulse systems, the signal source is often referred to as a target. "Target" is used as a generic term for all types of sources.

The angle between the receive beam axis and a line to the target is determined from a sum signal (Σ) and a difference signal (Δ). The sum signal Σ is the sum of all the energy reaching the antenna in the operating frequency range of the receiver with possible weighting for sidelobe reduction. The difference signal Δ is the difference between the signals from the two halves of the antenna, again with possible weighting for sidelobe reduction. Normally, separate azimuth and elevation angle signals are generated by the monopulse signal processor. In order to generate these angle signals there must be a difference signal for the azimuth direction (Δ_(A)) and another (separate) difference signal for the elevation direction (Δ_(E)). The angle between a signal source or target and the beam axis in one coordinate is determined from the ratio of the difference signal in that coordinate to the sum signal. This ratio is called the monopulse ratio and is here denoted ρ. For the elevation axis the monopulse ratio is denoted ρ_(E) and for the azimuth axis it is denoted ρ_(A). The angle between a target and the beam axis is a known function of ρ which is monotonic, depends on the antenna and its sidelobe weighting and possibly which axis and in many systems is close to being a linear function. Once a value of ρ is obtained the corresponding angle may be determined by calculation or by table look up. In those systems in which the function is strictly linear, the target angle is equal to Kρ where K is an antenna system dependent constant. Because the target angle is a known, predetermined function of the monopulse ratio, the performance of the radar is determined by the accuracy with which it determines the monopulse ratio. The present invention is primarily concerned with improvements in the accuracy of the determination of ρ and thus, via conversion of ρ to the corresponding target angle signal with improvements in the accuracy of the target angle signals.

A common (conventional) monopulse ratio is denoted ρ_(c) : ##EQU2## where Σ is the sum signal,

Δ is the difference signal,

γ=Σ_(I) Δ_(I) +Σ_(Q) Δ_(Q),

α=Σ_(I) ² +Σ_(Q) ²,

Σ_(I) is the in-phase component of Σ,

Σ_(Q) is the quadrature component of Σ,

Δ_(I) is the in-phase component of Δ, and

Δ_(Q) is the quadrature component of Δ.

This monopulse ratio ρ_(c) is accurately related to the actual target angle value when a monopulse system is operating in the clear with received signals having a large signal-to-noise ratio. "In the clear" means that the system is not being jammed and the received signal (the return signal in a radar system) is largely free of clutter and noise. As the signal-to-noise ratio of the received signal decreases, the accuracy of ρ_(c) decreases because noise signals become a more significant portion of the received signals from which the value ρ_(c) is derived. This reduces the contribution of the desired signal to the measured value of ρ_(c). When the signal-to-noise ratio becomes low enough, a determination of ρ_(c) based on a single received pulse is meaningless because the contribution of the noise signal essentially randomizes the value and any given value has an unknown relationship to the actual target angle. Under such conditions a value is determined from multiple pulses because, as is well-known, averaging over a number of repetitions of a noisy desired signal can produce a representation of that desired signal which is statistically more accurate than a representation based on a single occurrence of the signal. In the prior art such determinations based on multiple pulses have been made in either of two ways: (1) the result ρ_(c) for each pulse has been averaged over the desired number of pulses to provide a value which is the average of the ρ_(c) values; or (2) the values γ and α have been averaged separately for the desired number of pulses (yielding average values γ_(ave) and α_(ave)) and then γ_(ave) has been divided by α_(ave) to provide a value ρ_(c).sbsb.ave. Averaging a number of single pulse values of ρ_(c) for a desired number of pulses produces a noise estimate. This is because for a low enough signal-to-noise ratio the distribution of values for ρ_(c) does not have a finite variance and therefore the central limit theorem does not apply and averaging does not improve the measured value. Averaging γ and α and then dividing reduces the noise in the final result because α and γ each have a finite variance and the central limit theorem applies and the average of each of them (γ and α) individually does converge to a less noisy result. However, that less noisy result is strongly biased. This is because the noise power makes a positive contribution to α but not to γ. As a result, when γ_(ave) is divided by α_(ave) to obtain the multipulse value ρ_(c) ave, that result is smaller than it would have been if no noise were present. This smaller value corresponds to a smaller angle between the target and the beam axis. Thus, this bias is always inward toward the beam axis from the actual location of the signal source. As concern has increased for radar and communication system operation in high noise environments and in the presence of clutter and jamming, a need has developed for an ability to determine the angle of the signal source or target with respect to the beam axis with increased accuracy in response to a received signal having a low signal-to-noise ratio.

SUMMARY

In accordance with the present invention an improved monopulse signal processor is configured to perform processing steps in parallel and to use all of the energy in the received signals in deriving the monopulse ratio for a received signal. This processor is preferably configured to derive each monopulse ratio value from N successive received pulses. The resulting monopulse ratio for a general axis (azimuth or elevation) has the value: ##EQU3## where ##EQU4## where α_(i) is the value of α for the i^(th) pulse,

    α.sub.i =Σ.sub.Ii.sup.2 +Σ.sub.Qi.sup.2, ##EQU5## where β.sub.i is the value of β for the i.sup.th pulse,

    β.sub.i =Δ.sub.Ii.sup.2 +Δ.sub.Qi.sup.2 ##EQU6## where γ.sub.i is the value of γ for the i.sup.th pulse, and

    γ.sub.i =Σ.sub.Ii Δ.sub.Ii +Σ.sub.Qi Δ.sub.Qi.

This value of ρ is a maximum likelihood value of the monopulse ratio and hence of the angle between the beam axis and a line to the signal source or target in the plane to which the difference values (Δ) apply and has very little bias.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the specification of the position of a signal source relative to the antenna beam axis in terms of an elevation angle and an azimuth angle;

FIG. 2 is a functional block diagram of a signal processor system in accordance with the present invention in which the signals are processed digitally;

FIG. 3 is a functional block diagram of the signal processing computer included in FIG. 2;

FIG. 4 is a flow chart of a preferred manner of processing the signals in the FIG. 3 system;

FIG. 5 is a functional block diagram of an alternative configuration for the signal processing computer; and

FIG. 6 is a flow chart of a manner of processing the signals in the FIG. 5 system.

In FIG. 1 a monopulse receiving antenna 10 has a center 11, an antenna axis which lies along line 12 and a beam axis which lies along the line 13. In many reflector antenna systems the lines 12 and 13 always coincide. In many phased array antennas the lines 12 and 13 only coincide for one beam pointing angle and diverge for all others. A signal source or target 14 lies on a line 16 from the antenna center. As viewed from the antenna center 11, the target 14 is displaced from the beam axis by an azimuth angle φ and by an elevation angle θ. The angles φ and θ are determined in a monopulse radar system by monopulse processing of the sum, azimuth difference and elevation difference signals returned from the target 14. The antenna 10 provides a sum signal (Σ), an azimuth difference signal (Δ_(A)) and an elevation difference signal (Δ_(E)). These signals are coupled to a monopulse signal processing system 30.

The presence of a target somewhere in the antenna beam is determined by a target detection portion of the signal processor. The target detection processor receives and processes the sum beam or sum and difference beams to detect target reflections. The present invention is not directly concerned with the target detection portion of the signal processor. The time elapsed between the emission of the radar pulse and the detection of the reflection from a target provides a measure of the range from the antenna to the target. In order to specify the location of that target, it is necessary to determine the azimuth and elevation angles of the target with respect to the beam axis (the position of the beam axis is known). It is this angle determination aspect of a monopulse system with which the present invention is directly concerned. The azimuth and elevation angles of the location of the detected target (relative to the beam axis) are derived by monopulse processing of the portions of the received beams (Σ, Δ_(A) and Δ_(E)) which produced the target detection signal.

When the signal-to-noise ratio in the received beam is small, accurate monopulse ratios and thus target location angles can not be determined from a single return pulse. Integration over a number of pulses is desired in order to reduce the effect of the noise contribution to the target angle determinations.

We have determined that the prior art process discussed above at equation 1 is not optimum for this purpose. First, as discussed above, the resulting answer is either noisy or biased. Second, that process does not make use of all of the available target energy in the received signals. In accordance with the present invention, the following monopulse ratio ρ makes use of all of the available target energy in the received signals, is successful in reducing the noise level and is unbiased: ##EQU7## where ##EQU8## where α_(i) is the value of α for the i^(th) pulse,

    α.sub.i =Σ.sub.Ii.sup.2 +Σ.sub.Qi.sup.2, ##EQU9## where β.sub.i is the value of β for the i.sup.th pulse,

    β.sub.i =Δ.sub.Ii.sup.2 +Δ.sub.Qi.sup.2, ##EQU10## where γ.sub.i is the value of γ for the i.sup.th pulse, and

    γ.sub.i =Σ.sub.Ii Δ.sub.Ii +Σ.sub.Qi Δ.sub.Qi.

This α and this γ have the same definitions as in the prior art estimate ρ_(c). To simplify expression No. 2, (β-α) is defined as being equal to η. Expression No. 2 may then be rewritten as: ##EQU11##

Physically, α is a measure of the sum beam power, β is a measure of the difference beam power, γ is a measure of the correlation between the sum beam power and the difference beam power and η is a measure of the difference between the power in the difference beam and the power in the sum beam. Thus, the prior art monopulse ratio ρ_(c) is proportional to the correlation of the sum and difference beam powers divided by the sum beam power. The inventive monopulse ratio ρ is proportional to the difference between the power in the difference beam and the power in the sum beam divided by the correlation of the sum and difference beam powers (η_(T) /2γ_(T)) plus a correction term ##EQU12##

A monopulse processing system 30, which in accordance with the present invention provides such a monopulse ratio is illustrated in functional block form in FIG. 2. A signal processor in accordance with this invention may operate in either an analog or digital manner, in accordance with its construction. However, a digital processor is preferred.

The monopulse processing system 30 includes a receiver and matched filter system 22 for correlating the received signal with a transmitted coded signal. Depending on the particular designs employed, the receiver and matched filter may be distinct systems connected in series or portions of the matched filter may be distributed within the receiver. Alternatively, where an uncoded signal is transmitted a receiver without a matched filter may be used. The output from the receiver and matched filter system 22 is six signals. These are the azimuth difference in-phase signal (Δ_(AI)), the azimuth difference quadrature signal (Δ_(AQ)), the sum in-phase signal (Σ_(I)), the sum quadrature signal (Σ_(Q)), the elevation difference in-phase signal (Δ_(EI)), and the elevation difference quadrature signal (Δ_(EQ)). The six outputs from system 22 are connected to a bank 32 of six analog-to-digital converters (ADCs) 32₁ -32₆. In response to timing signals from a controller 90, the bank of A-to-D converters 32 simultaneously converts the amplitude of each of the six signals from the matched filter into six separate binary (digital) values. In a typical system, the bank of A-to-D converters 32 may provide each amplitude in the form of a seven bit magnitude and a sign bit. The resulting eight-bit outputs can range in value from minus 128 to plus 128. Each time the controller activates the A-to-D converters, each of these converters provides a new value at its output and as a group these A-to-D converters together provide a new set of these six values. If digital beam forming is employed in a phased array antenna, then the digital beamformer provides the same six outputs. Those outputs from the digital beamformer are then used in place of the six outputs from the ADCs 32. In either event, the set of six values is provided to a target detection processor 34 for use in determining whether a target is present in the portion of the return signal to which these digital values correspond. The same digital values are also provided to a monopulse signal processing computer 40 which in accordance with the present invention provides as outputs values of φ and θ which are the angles between the line 16 to the target 14 and the antenna beam axis 12 in the azimuth direction and the elevation direction, respectively.

Detection processor 34 determines whether the received values indicate the presence of a target. If they do, then the detection processor 34 provides to tracker 95 a detected-target signal which specifies the range of the target. If they do not, then either no signal or a no-target signal is provided to tracker 95 by detection processor 34.

The monopulse signal processing computer 40 provides a set of target angle signals to tracker 95 for each set of received input values. These target angle signals specify the angle between the beam axis and the target in the event that the processed values include target energy. If tracker 95 receives a detected-target signal in conjunction with a set of the target angle signals, then tracker 95 determines the target position from the known beam position in combination with the determined range and azimuth and elevation target angles. The tracker then determines whether this target location is a newly detected target or is the new position of an old target. If it is a new target, the tracker establishes a new target track to begin following this target. If it is a new position of an old target, then this new position is used to update the track on that old target by providing this new position as the most recent target location. When no detected-target signal or a no-target signal is received in conjunction with a set of target angle signals, tracker 95 discards those angle signals without further processing. Both the target detection processor 34 and the tracker 95 are conventional, the present invention being concerned with the monopulse signal processing computer 40 which converts the received digital values to their corresponding monopulse ratios and then to target angles.

Monopulse signal processing computer 40 is shown in functional block form in FIG. 3. The monopulse processor 40, has six input terminals D₁ through D₆. Each of these terminals is designed to be connected to receive the output of a corresponding one of the six A-to-D converters 32₁ -32₆.

Computer 40 is designed to process data in parallel in order to minimize the time required to derive the monopulse ratios ρ_(A) and ρ_(E) and thus the target angles φ and θ, respectively. To this end, the functional blocks which perform the early steps in data reduction are arranged in successive ranks. The first rank operates on data received from the A-to-D converters 32. Each of the other ranks operates on the output from the previous rank. The operations within a given rank are performed in unison in order that each rank may receive all of its inputs at the same time.

In the configuration illustrated, the input terminal D₁ is designed to receive the digitized value of the in-phase azimuth difference signal Δ_(AI) (from ADC 32₁), the input terminal D₂ is designed to receive the digitized value of the quadrature difference signal Δ_(AQ) (from ADC 32₂), the input terminal D₃ is designed to receive the digitized value of the in-phase sum signal Σ_(I) (from ADC 32₃), the input terminal D₄ is designed to receive the digitized value of the quadrature sum signal Σ_(Q) (from ADC 32₄), the input terminal D₅ is designed to receive the digitized value of the in-phase elevation difference signal Δ_(E1) (from ADC 32₅) and the input terminal D₆ is designed to receive the digitized value of the quadrature elevation difference signal Δ_(EQ) (from ADC 32₆).

The first rank of processing circuits within processor 40 comprises six squaring circuits or squarers 42₁ -42₆ and four two-input multiplying circuits 44₁ -44₄. The D₁ input (Δ_(AI)) is coupled to the input of the first squarer 42₁ and to one input of the first multiplier 44₁. The D₂ input (Δ_(AQ)) is coupled to the second squarer 42₂ and to one input of the second multiplier 44₂. The D₃ input (Σ_(I)) is coupled to the input of the third squarer 42₃, to the other input of the first multiplier 44₁ and to one input of the third multiplier 44₃. The D₄ input (Σ_(Q)) is coupled to the input of the fourth squarer 42₄, to the other input of the second multiplier 44₂ and to one input of the fourth multiplier 44₄. The D₅ input (Δ_(EI)) is coupled to the input of the fifth squarer 42₅ and to the other input of the third multiplier 44₃. The D₆ input (Δ_(EQ)) is coupled to the input of the sixth squarer 42₆ and to the other input of the fourth multiplier 44₄.

The second rank of processing circuits within processor 40 comprises five two-input adders 46₁ -46₅ configured to receive the ten output values from the first rank processing circuits. The outputs (Δ_(AI) ² and Δ_(AQ) ²) of the first two squarers 42₁ and 42₂ are coupled to the inputs of the first adder 46₁. The output of adder 46₁ is a value β_(A), which is equal to Δ_(AI) ² +Δ_(AQ) ². The outputs (Σ_(I) ² and Σ_(Q) ²) of the third and fourth squarers 42₃ and 42₄ are coupled to the inputs of the second adder 46₂. The output of adder 46₂ is a value α which is equal to Σ_(I) ² +Σ_(Q) ². The outputs (Δ_(EI) ² and Δ_(EQ) ²) of the fifth and sixth squarers 42₅ and 42₆ are coupled to the inputs of the third adder 46₃. The output of adder 46₃ is a value β_(E) which is equal to Δ_(EI) ² +Δ_(EQ) ². The outputs (Σ_(I) Δ_(AI) and Σ_(Q) Δ_(AQ)) of the first two multipliers 44₁ and 44₂ are coupled to the inputs of the fourth adder 46₄. The output of the adder 46₄ is a value γ_(A) which is equal to Σ_(I) Δ_(AI) +Σ_(Q) Δ_(AQ). The outputs (Σ_(I) Δ_(EI) and Σ_(Q) Δ_(EQ)) of the two multipliers 44₃ and 44₄ are coupled to the inputs of the fifth adder 46₅. The output of adder 46₅ is a value γ_(E) which is equal to Σ_(I) Δ_(EI) +Σ_(Q) Δ_(EQ).

The third rank of processing circuits comprises two two-input adders 48₁ and 48₂ and two times-two multipliers 50₁ and 50₂. The adders 48₁ and 48₂ each complement one input to provide an output which is the difference between their two inputs. The adder 48₁ has the value β_(A) from adder 46₁ coupled to its normal or non-complementing input and the value α from adder 46₂ coupled to its complementing or negative input. The output of the adder 48₁ is a value η_(A) which is equal to β_(A) -α. In a similar manner, the second adder 48₂ has the value β_(E) coupled to its positive input, and the signal α coupled to its complementing input and provides a value η_(E) equal to β_(E) -α at its output. The first times-two multiplier 50₁ receives the output of the adder 46₄ (γ_(A)) as its input and provides the value 2γ_(A) as its output. In a similar manner, the second times-two multiplier 50₂ receives the output of the adder 46₅ as its input and provides the value 2γ_(E) as its output.

The first three ranks of processing circuits in the signal processor 30 (extending from the inputs D₁ -D₆ through the adders 48₁ and 48₂ and the multipliers 50₁ and 50₂) convert each set of six input data values into a corresponding set of four reduced data values (η_(A), η_(E), 2γ_(A) and 2γ_(E)). These reduced data values may be used to determine the monopulse ratios and target angles for the azimuth and elevation directions based on that single set of six input values. However, in accordance with the present invention, it is preferred to accumulate N of these sets of reduced data values and to determine angles based on N of each of them. This accumulation is done in the fourth rank of processing circuits.

The fourth rank of processing circuits comprises four two-input adders 52₁ -52₄ and four associated memories 54₁ -54₄. Each adder 52 is connected to receive its first input from a first output of its associated memory 54 and to provide its output as an input to that same memory. The second input of adder 52₁ is connected to receive the output of adder 48₁. The second input of the adder 52₂ is connected to receive the output of the multiplier 50₁. The second input of the adder 52₃ is connected to receive the output of multiplier 50₂ and the second input of adder 52₄ is connected to receive the output of adder 48₂. The number N of sets of input values over which the reduced data values η_(A), η_(E), 2γ_(A) and 2γ_(E) are accumulated is determined by the control system 90.

During this accumulation process, the stored value in each of the memories 54₁ -54₄ is provided at its first output. Once the η and 2γ values for the final set of inputs to be accumulated in a given accumulation cycle have been included in the values stored in the memories 54, the stored values are provided at the second outputs of the memories 54. The combination of an adder 52 and its associated memory 54 function as an accumulating adder and could be replaced by an accumulating adder. However, that would limit the efficiency of signal processing computer 40 by restricting it to accumulating η and 2γ values for a single range segment per pulse. With the illustrated system, each memory 54 can be provided with as many registers as there are range cells of interest per transmitted pulse. By providing the accumulated value for each range cell from memory 54 to the adder 52 for addition of the new data for that range cell, all range cells of interest can be processed on each pulse. The second output of each memory 54₁ -54₄ is coupled to the input of a separate associated memory 62₁ -62₄, respectively. The memories 62 comprise the fifth rank of processing circuits. Once the final values for an accumulation cycle have been transferred from the memories 54 to the memories 62, the memories 54 are cleared in preparation for another accumulation cycle. In this specification, the accumulated total values which are stored in the memories 62 are indicated by a "T" as a final subscript. Thus, the value stored in memory 62₁ is η_(AT) which is the accumulated total η value for the azimuth beam for the N pulses of interest.

The next (sixth) rank of processing circuits comprises four squarers 64₁ -64₄. Each of these is connected to receive the value stored in the corresponding memory 62. The outputs of these four squarers are η_(AT) ², 4γ_(AT) ², η_(ET) ² and 4γ_(ET) ².

Through the sixth rank of processing circuits, values which are subsequently combined in the process of producing the monopulse ratios ρ_(A) and ρ_(E) and target angles φ and θ are processed in parallel. From the outputs of the sixth rank (squarers 64) onward the production of each target angle is a serial process. Since the processing of the azimuth signal is identical to the processing of the elevation signal in the serial portion of the process, only the azimuth hardware will be described in detail. The elevation hardware is identical except for the subscripts on its reference numerals which are 2's instead of 1's.

A two-input adder 70₁ has its inputs connected to receive the outputs of the squarers 64₁ and 64₂. The output of this adder is (η_(AT) ² +4γ_(AT) ²) and is connected to the input of a corresponding square root extractor 72₁. The output of the square root extractor 72₁ is √η_(AT) ² +4γ_(AT) ² . The output of the square root extractor 72₁ is connected to the first input of an adder 74₁ whose other input is connected to receive the value η_(AT) from memory β₁. The output of this adder is η_(AT) +√4γ_(AT) ² +η_(AT) ² . The output of the adder 74₁ is connected to the input of a divider 76₁ as its dividend. The divisor input of the divider 76₁ is connected to receive the value 2γ_(AT) from the memory 62₂. The output of the divider 76₁ is the monopulse ratio ρ_(A) for the azimuth direction. The value of ρ_(A) is used as the address for a read only memory (ROM) 78₁ which provides as its output the azimuth target angle φ which corresponds to the value of ρ_(A) by which it is addressed. ROM 78₂ is similar except that it provides as its output the elevation target angle θ which corresponds to the value of η_(E) by which it is addressed. The value stored in the ROM takes into consideration constants for the particular antenna and therefore the same value of ρ may result from different target angles for azimuth and elevation.

For speed of processing and to limit the complexity of the hardware for determining these ratios, it is preferred to do complicated (time consuming) computations by table look up rather than by direct computation. This produces much faster processing than doing the actual calculations for each input value and is facilitated by the limited number of bits in the digital outputs of the ADCs 32.

At each stage in the processing where the number of bits in the answer is a substantial increase over the number of bits in the input such as occurs in squaring and in multiplying numbers, it is preferred, in order to minimize the complexity of the following circuitry, to truncate the answers at a number of bits which provide the required degree of accuracy without carrying unneeded bits. Thus, rather than carrying 16 bit answers into the second rank adders, it is preferred to only carry 8-bit answers. Such truncation has a significant effect on the size of the table look up system which is used as the squarer 64. In a similar manner, the outputs of the squarers 64 are preferably truncated to retain only the number of bits necessary to obtain the required degree of resolution. This is done by only storing that number of bits in the ROM which is used to provide these table look up values. The square root extractors 72 are again implemented in a table look-up form. The dividers 76 may be implemented in a table look up form where the addressing of the table requires two indices, one being the divisor, 2γ_(T) and the other being the dividend (η_(T) +√4γ_(T) ² +η_(T) ² ). The number of bits in the estimate of ρ depends on the maximum angle resolution desired. An 8-bit value for ρ provides adequate resolution for many systems.

It will be understood that in accordance with the processing capabilities of the signal processing computer, the functions of several elements such as adders or memories may be provided by a single element in the signal processor.

A flow diagram 100 of the preferred process in the monopulse signal processing system 30 is illustrated in FIG. 4. The signal processing of a set of N pulses begins in step 110 with the initialization of the indices and resetting of the values of η_(AT), 2γ_(At), η_(Et) and 2γ_(Et) to zero. That is, the contents of the memories 54 in FIG. 3 are set to 0. The index i ranges from 1 to N and is the number of the pulse currently being processed within a group of N pulses. The value of i is reset to 1 each time a new group of N pulses is to be collected. The η_(AT), 2γ_(At), η_(Et) and 2γ_(Et) are the values currently in the memories 54 at any time in the process. In step 112 a sample of each of the signals from the matched filter is converted to a digital value. These values are coupled into the processor 40 as the inputs D₁ -D₆. In step 114, ten substeps 114₁ -114₁₀ take place simultaneously in the first rank of hardware of FIG. 3. Step 114₁ derives the square of the first input which is (Δ_(AI))². Step 114₂ derives the square of the second input which is (Δ_(AQ))². Step 114₃ derives the square of the third input which is (Σ_(I))². Step 114₄ derives the square of the fourth input which is (Σ_(Q))². Step 114₅ derives the square of the fifth input which is (Δ_(EI))². Step 114₆ derives the square of the sixth input which is (Δ_(EQ))². Simultaneously, step 114₇ derives the product of the first input value times the third input value which is Δ_(AI) Σ_(I), step 114₈ derives the product of the second and fourth input values which is Δ_(AQ) Σ_(Q), step 114₉ derives the product of the third input times the fifth input which is Σ_(I) Δ_(EI), and step 114₁₀ derives the product of the fourth input times the sixth input which is Σ_(Q) Δ_(QE).

In step 116 five substeps 116₁ -116₅ take place simultaneously. Each of these substeps is an addition step which adds together two of the results of the steps 114. Step 116₁ adds the results of the steps 114₁ and 114₂ to produce an output β_(A) which is (Δ_(AI) ² +Δ_(AQ) ²), step 116₂ operates on the results of steps 114₃ and 114₄ to produce an output α equal to (Σ_(I) ² +Σ_(Q) ²) and step 116₃ operates on the results of the steps 114₅ and 114₆ to produce an output β_(E) which is (Δ_(EI) ² +Δ_(EQ) ²). Simultaneously step 116₄ operates on the results of steps 114₇ and 114₈ to produce the signal γ_(A) which is equal to (Δ_(AI) Σ_(I) +Δ_(AQ) Σ). Step 116₅ combines the results of steps 114₉ and 114₁₀ to produce the signal γ_(E) which is (Σ_(I) Δ_(EI) +Σ_(Q) Δ_(EQ)).

In step 118 four sub-steps 118₁ -118₄ take place simultaneously. In sub-step 118₁ the result of step 116₂ is subtracted from the result of step 116₁ to produce the value η_(A) which is equal to (β_(A) -α). In step 118₂ the result of step 116₂ is subtracted from the result of step 116₃ to produce the value η_(E) which is equal to (β_(E) -α). In sub-step 118₃ the result of step 116₄ is multiplied by 2 to yield the value 2γ_(A) and in step 118₄ the result of sub-step 116₅ is multiplied by 2 to produce the value 2γ_(E).

In step 120, four additions take place simultaneously. In step 120₁ the result of step 118₁ is added to the stored value of η_(At). On the first cycle, that previously stored value is zero as the result of the initialization performed in step 110. In step 120₂ the result of step 118₂ is added to the stored value of η_(Et). In step 120₃ the result of step 118₃ is added to the accumulated value of 2γ_(AT) and in step 120₄ the result of step 118₄ is added to the accumulated value of 2γ_(Et).

In step 122 the value of the index i is compared with N (the number of pulses over which the data is to be accumulated). If i is not equal to N, then the process proceeds to step 124 which increments i by 1. From step 124 the process returns to step 112 to convert another sample of each of the six input signals to digital values to be processed through steps 114-122. If in step 122, i is found to be equal to N, then the process proceeds to step 126.

In step 126 the accumulated values of the variables η_(At), 2γ_(At), η_(Et) and 2γ_(Et) are transferred to storage in the memories 62 of FIG. 3 in the four substeps 126₁ -126₄. The process then branches to flow in two separate portions simultaneously. The first of these branches returns the data accumulation portion of the process to step 110 which initializes that portion of the process by setting i equal to 1 and resetting the values of η_(At), ² γ_(At), η_(Et) and 2γ_(Et) to zero. The other branch proceeds by further processing the accumulated values which were stored in step 126. In step 128 each of the four values which were stored in step 126 is squared in a different one of the substeps 128₁ -128₄. The squaring of the two azimuth values takes place in steps 128₁ and 128₂ while the squaring of the elevation values takes place in steps 128₃ and 128₄. In step 130₁ the results of steps 128₁ and 128₂ are added together to produce the value (4γ_(AT) ² +η_(AT) ²). Simultaneously in step 130₂ the results of steps 128₃ and 128₄ are added together to produce the result (4γ_(ET) ² +η_(ET) ²). In steps 132₁ and 132₂ the square root of the result of the corresponding addition step 130 is extracted. In step 134₁ this result is added to the η_(AT) value which is derived from the memory 62₁ to yield a value η_(AT) +√4γ_(AT) ² +η_(AT) ² . In step 136₁ the result of the addition of step 134₁ is divided by the value 2γ_(AT) which is derived from the storage register 62₂. The result of the division step 136₁ is the value ρ_(A) which is the azimuth monopulse ratio. In step 140₁, the azimuth angle φ between the beam axis and the target for this set of N pulses is derived from a lookup table using ρ_(A) or from a direct calculation using scale factors and powers of ρ_(A). This may be accomplished by a ROM addressed by the value of ρ_(A). This completes the process of deriving the angle φ. Steps 134₂, 136₂ and 140₂ are similar to steps 134₁, 136₁ and 140₁, except for operating on elevation data rather than azimuth data and providing the elevation angle θ.

As was explained previously, the resulting θ and φ values are passed to the tracking system 95 to update the track on the target. This process continues as long as the target continues to be detected and to be within the area of interest. Upon completion of the calculations for the accumulated series of pulses the angles φ and θ to the target in the azimuth and elevation coordinates, respectively are provided to tracker 95. Detection processor 34 provides the range of this target to tracker 95, if processor 34 has detected a target.

In accordance with the processing power of the computer in which this digital processing is performed, the location of a number of distinct targets or signal sources may be determined simultaneously. Thus, the angle of a second target or signal source 15 in FIG. 1 at a different (greater) range may be determined simultaneously in accordance with the time of return of the data used in determining the position of each of the targets or signal sources.

The inventive process provides accurate target angle information both for steady targets and fluctuating targets so long as the signal return level is adequate for the integration process to separate the desired signal from noise. This inventive process provides an accurate target location when it is derived from a single pulse even though its equation (Equation 2) does not reduce to the prior art single pulse formulation (Equation 1). However, the primary benefit of this inventive process is in the processing of a number of low signal-to-noise pulses to provide an integrated angle value since this value is more accurate than the conventional value.

In the prior art angle estimate ρ_(c) =γ/α, the numerator of the fraction goes to zero for targets on the beam axis but the denominator does not. The sign of ρ_(c) changes as a target crosses the axis. In the present process the sign of the estimate also changes on crossing the beam axis. The present process tends toward a division of zero by zero for targets near the beam axis because both the numerator and the denominator go to zero. This condition can be tested for prior to performing the division operation. When the quotient of the division becomes large due to division by too small a divisor and a target has been detected, that target may be declared to be on the beam axis for the coordinate (azimuth or elevation) in question. It is because of the problem of division by too small a number that the division operation 136 is preferably performed as the final step in the derivation of the value of ρ. This enables a direct comparison of the values of the divisor and dividend to be used to determine the presence of an on-axis target.

There are alternatives to setting the ratio to zero when 2γ_(T) is too small. Under some circumstances depending on the number of pulses (N) being processed and the signal-to-noise ratio, the conventional estimate is more accurate for very small angles. Therefore, one alternative is to establish a threshold value V and provide that ρ is set to γ_(T) /α_(T) whenever 4γ_(T) ² <V. The value of V may be chosen to be 4 or 16 where seven bit data values ranging from -128 to +128 are provided as inputs to monopulse processing computer 40. Processing for this alternative can be in accordance with modified versions of any of the methods already described.

FIG. 5 is similar to FIG. 4 in steps 110; 112; 114; 116; 118₁ -118₄ ; 120₁ -120₄ ; 122; 124; 126₁ -126₄ ; 128₁ -128₄. In addition, FIG. 4 includes a step 118₅ in which α is multiplied by two to produce the value 2α. In step 120₅ 2α_(t) is set equal to 2α_(t) +2.sub.α in order to provide an accumulated value of 2α_(t). When the N pulses have accumulated step 126₅ sets 2α_(T) equal to 2α_(t) and stores that value of 2α_(T). Step 129₁ determines whether step 138₁ or steps 130₁, 132₁, 134₁ and 136₁ are performed. If in step 129₁ 4γ_(AT) ² ≧V, then steps 130₁, 132₁, 134₁ and 136₁ are performed and step 138₁ is not performed. If 4γ_(AT) ² <V then step 138₁ is performed and steps 130₁, 132₁, 134₁ and 136₁ are not performed. Step 138₁ divides the stored value 2γ_(AT) by the stored value 2α_(T) and the resultant value is the monopulse ratio ρ_(A). Steps 129₂, 130₂, 132₂, 134₂, 136₂ and 138₂ are similar except for operating on elevation data rather than azimuth data. In each case the corresponding step 140 converts the value of ρ to the corresponding target angle.

FIG. 6 illustrates a modified version 40' of the monopulse signal processing computer 40 which is suitable for running the modified process 100'. Processor 40' is like processor 40 except for the addition of hardware 80 for processing the α values to obtain a value 2α_(T) and the addition of hardware 82₁ and 82₂ for checking the threshold condition for the azimuth and elevation channels respectively and providing the value ##EQU13## when the value of 4γ_(T) ² for a channel is less than the threshold value V.

The threshold condition hardware 82₁ comprises a divider 84₁ for dividing the stored value 2γ_(AT) by the value 2α_(T) to produce the conventional angle estimate ρ_(c) =γ/α, and a comparator 86₁ and a switch 88₁ for controlling whether the estimate ρ_(A) from divider 76₁ or the estimate ρ_(c) from divider 84₁ is provided at the output terminal. The hardware 82₂ is identical hardware 82₁ except for the subscripts on the reference numerals. 

What is claimed is:
 1. In a monopulse signal processing system of the type which receives an in-phase difference signal (Δ_(I)) and a quadrature difference signal (Δ_(Q)) in a first coordinate and an in-phase sum signal (Σ_(I)) and a quadrature sum signal (Σ_(Q)), all derived from an antenna system and which provides target tracking information with respect to a target which is a source of at least some of the energy in said received signals and in the process converts each of said received signals to a series of digital signals, each representative of an instantaneous amplitude of that received signal and derives from those digital signals a first monopulse ratio signal which corresponds to the angle in said first coordinate between the receive beam axis of said antenna system and a line to said target, and said system is of the type which includes means responsive to said Σ_(I) and Σ_(Q) digital signals for providing a digital signal α which is the sum of their squares (Σ_(I) ² +Σ_(Q) ²), means responsive to said Σ_(I), Σ_(Q), Δ_(I) and Δ_(Q) digital signals for providing a digital signal γ which is the sum of the product of said Σ_(I) and Δ_(I) signals and the product of said Σ_(Q) and Δ_(Q) signals (Σ_(I) Δ_(I) +Σ_(Q) Δ_(Q)), the improvement comprising:means responsive to said Δ_(I) and Δ_(Q) digital signals for providing a digital signal β which is the sum of their squares (Δ_(I) ² +Δ_(Q) ²); and means for deriving said first monopulse ratio signal from said α, β and γ digital signals.
 2. The improvement recited in claim 1 wherein said means for deriving includes:means responsive to said α and β digital signals for providing a digital signal η which is their difference (β-α); means responsive to said η signal for providing a signal η² ; means responsive to said γ digital signal for providing a digital signal 2γ and a digital signal 4γ² ; means responsive to said η² and 4γ² digital signals for providing a digital signal which is the square root of their sum (√η² +4γ² ); means responsive to said √η² +4γ² digital signal and said η digital signal for providing a digital signal which is their sum (η+√η² +4γ² ); and means responsive to said (η+√η² +4γ² ) digital signal and said 2γ digital signal for providing a digital signal ρ whose value is (η+√η² +4γ² ) divided by 2γ, said ρ signal being provided as said first monopulse ratio signal.
 3. The improvement recited in claim 2 wherein:said means responsive to said η signal comprises a first accumulating adder means responsive to said η signal for each of N pulses for providing a signal η_(T) which is their sum; said means responsive to said γ signal comprises a second accumulating adder means responsive to said 2γ signal for each of said N pulses for providing a signal γ_(T) which is their sum, whereby said target angle signal depends on the received signals from said N pulses.
 4. The improvement recited in claim 3 wherein said processing system also includes:means for converting said monopulse ratio signal into a target angle signal specifying said corresponding angle.
 5. The improvement recited in claim 2 wherein said processing system also includes:means for receiving in-phase and quadrature difference signals in a second co-ordinate; means responsive to said second co-ordinate signals for deriving a second monopulse ratio signal, which corresponds to the angle in said second co-ordinate between said receive beam axis and said line to said target; and means for providing said second monopulse ratio signal at an output.
 6. The improvement recited in claim 2 further comprising means for comparing said 4γ² signal with a threshold value and means for providing a monopulse ratio signal equal to γ/α whenever said 4γ² signal is less than said threshold value.
 7. A monopulse method of processing received radio signals to provide a signal ρ which is a measure of the angle in a first coordinate between the receive beam axis of an antenna and a line to a target from which the antenna receives energy, said method comprising the steps of:(a) processing signals received from said antenna to provide digital signals representative of the instantaneous amplitudes of in-phase and quadrature difference signals (Δ_(I) and Δ_(Q), respectively) in said first coordinate and in-phase and quadrature sum signals (Σ_(I) and Σ_(Q), respectively); (b) squaring said Σ_(I), Σ_(Q), Δ_(I) and Δ_(Q) signals and adding them to provide a digital signal η equal to Δ_(I) ² +Δ_(Q) ² -Σ_(I) ² -Σ_(Q) ² ; (c) multiplying said Σ_(I) signal by 2 times said Δ_(I) signal and said Σ_(Q) signal by 2 times said Δ_(Q) signal and adding them to provide a digital signal 2γ equal to 2Σ_(I) Δ_(I) +2Σ_(Q) Δ_(Q) ; and (d) squaring said η and 2γ signals and adding them to provide a signal equal to √η² +4γ² ; and (e) extracting the square root √η² +4γ² (f) adding η to said square root and dividing by 2γ to provide a signal equal to ##EQU14## as said ρ signal.
 8. The method recited in claim 7 further comprising performing the following steps prior to step (d):(g) accumulating a sum of the signals η from each of N received pulses; and (h) accumulating a sum of the signals 2γ from each of said N received pulses whereby the signal ρ depends on said N received pulses.
 9. The method recited in claim 7 further comprising the steps of:comparing the 4γ² signal with a threshold value; and providing as said ρ signal the value γ/α when 4γ² is less than said threshold value. 